##
**Bayesian causal mediation analysis with multiple ordered mediators.**
*(English)*
Zbl 07289550

Summary: Causal mediation analysis provides investigators insight into how a treatment or exposure can affect an outcome of interest through one or more mediators on causal pathway. When multiple mediators on the pathway are causally ordered, identification of mediation effects on certain causal pathways requires a sensitivity parameter to be specified. A mixed model-based approach was proposed in the Bayesian framework to connect potential outcomes at different treatment levels, and identify mediation effects independent of a sensitivity parameter, for the natural direct and indirect effects on all causal pathways. The proposed method is illustrated in a linear setting for mediators and outcome, with mediator-treatment interactions. Sensitivity analysis was performed for the prior choices in the Bayesian models. The proposed Bayesian method was applied to an adolescent dental health study, to see how social economic status can affect dental caries through a sequence of causally ordered mediators in dental visit and oral hygiene index.

### MSC:

62-XX | Statistics |

PDF
BibTeX
XML
Cite

\textit{T. Gao} and \textit{J. M. Albert}, Stat. Model. 19, No. 6, 634--652 (2019; Zbl 07289550)

Full Text:
DOI

### References:

[1] | Albert, JM (2008) Mediation analysis via potential outcomes models. Statistics in Medicine, 27, 1282-1304. |

[2] | Albert, JM, Nelson, S (2011) Generalized causal mediation analysis. Biometrics, 67, 1028-38. · Zbl 1226.62104 |

[3] | Kenny, DA (1986) The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psycho- logy, 51, 1173-82. |

[4] | Daniel, RM, De Stavola, BL, Cousens, SN, Vansteelandt, S (2015) Causal mediation analysis with multiple mediators. Biom- etrics, 71, 1-14. · Zbl 1419.62331 |

[5] | De Stavola, BL, Daniel, RM, Ploubidis, GB, Micali, N (2015) Mediation analysis with intermediate confounding: Structural equation modeling viewed through the causal inference lens. American Journal of Epidemiology, 181, 64-80. |

[6] | Imai, K, Keele, L, Yamamoto, T (2010) Identi- fication, inference and sensitivity analysis for causal mediation effects. Statistical Science, 25, 51-71. · Zbl 1328.62478 |

[7] | Imai, K, Yamamoto, T (2013) Identification and sensitivity analysis for multiple causal mechanisms: Revisiting evidence from framing experiments. Political Analysis, 21, 141-71. |

[8] | Little, RJ (2006) Calibrated Bayes: A Bayes/fre- quentist roadmap. American Statistician, 60, 213-23. |

[9] | MacKinnon, DP (2000) Contrasts in multiple mediator models. In Multivariate Applica- tions in Substance Use Research: New Methods for New Questions, edited by JS Rose, book section 5, pages 141-60. Mahwah, NJ: Lawrence Erlbaum Associates, Inc. |

[10] | Park, S, Kaplan, D (2015) Bayesian causal mediation analysis for group randomized designs with homogeneous and heteroge- neous effects: Simulation and case study. Multivariate Behavioral Research, 50, 316-33. |

[11] | Pearl, J (2001) Direct and indirect effects. In Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, edited by J Breese and D Koller, pages 411-20. San Francisco, CA: Morgan Kaufmann Publishers Inc. |

[12] | Pearl, J (2012) The mediation formula: A guide to the assessment of causal pathways in nonlinear models. In Causality: Statistical Perspectives and Applications, edited by C Berzuini, P Dawid and L Bernardinelli, book section 12, pages 151—79. Chichester: John Wiley and Sons, Ltd. |

[13] | Raftery, AE, Lewis, SM (1995) The number of iterations, convergence diagnostics and generic metropolis algorithms. In Practical Markov Chain Monte Carlo, edited by WR Gilks, D Spiegelhalter and S Richardson, pages 115-130. London: Chapman and Hall. |

[14] | Robins, JM (1986) A new approach to causal inference in mortality studies with a sustained exposure period: Application to control of the healthy worker survivor effect. Mathematical Modelling, 7, 1393-1512. · Zbl 0614.62136 |

[15] | Robins, JM (1989) The analysis of randomized and nonrandomized aids treatment trials using a new approach to causal inference in longitudinal studies. In Health Services Research Methodology: A Focus on AIDS, edited by Sechrest, L, Freeman, HE, Mulley, AG , pages 113-59. Washington, DC: U.S. Dept. of Health and Human Services, National Center for Health Services Research and Health Care Technology Assessment. |

[16] | Robins, JM, Greenland, S (1992) Identifiability and exchangeability for direct and indirect effects. Epidemiology, 3, 143-55. |

[17] | Rubin, DB (1974) Estimating causal effects of treatments in randomized and nonran- domized studies. Journal of Educational Psychology, 66, 688-701. |

[18] | Taguri, M, Featherstone, J, Cheng, J (2015) Causal mediation analysis with multiple causally non-ordered mediators. URL https://doi.org/10.1177/0962280215615899 (last accessed 27 August 2018). |

[19] | Tanner, MA, Wong, HW (1987) The calcula- tion of posterior distributions by data augmentation. Journal of the American Statistical Association, 82, 528-40. |

[20] | Tchetgen, EJ, Shpitser, I (2012) Semipara- metric theory for causal mediation analysis: Efficiency bounds, multiple robustness, and sensitivity analysis. Annals of Statistics, 40, 1816-45. · Zbl 1257.62033 |

[21] | VanderWeele, TJ, Chiba, Y (2014) Sensitivity analysis for direct and indirect effects in the presence of exposure-induced mediator- outcome confounders. Epidemiology Biostatistics and Public Health, 11, e9027. |

[22] | VanderWeele, TJ, Vansteelandt, S (2009) Conceptual issues concerning mediation, interventions and composition. Statistics and Its Interface, 2, 457-68. · Zbl 1245.62177 |

[23] | VanderWeele, TJ, Vansteelandt, S (2014) Mediation analysis with multiple mediators. Epidemiologic Methods, 2, 95-115. · Zbl 1359.92009 |

[24] | VanderWeele, TJ, Vansteelandt, S, Robins, JM (2014) Effect decomposition in the presence of an exposure-induced mediator-outcome confounder. Epidemiology 25, 300-306. |

[25] | Wang, W, Nelson, S, Albert, JM (2013) Estimation of causal mediation effects for a dichotomous outcome in multiple-mediator models using the mediation formula. Statistics in Medicine, 32, 4211-28. |

[26] | Yuan, Y, MacKinnon, DP (2009) Bayesian mediation analysis. Psychological Methods, 14, 301-22. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.